Internal problem ID [5229]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 2. Solutions of differential equations. Supplemetary problems. Page
11
Problem number: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {2 y^{\prime } x^{3}-y \left (y^{2}+3 x^{2}\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 44
dsolve(2*x^3*diff(y(x),x)=y(x)*(y(x)^2+3*x^2),y(x), singsol=all)
\begin{align*} y = \frac {\sqrt {\left (-x +c_{1} \right ) x}\, x}{-x +c_{1}} y = -\frac {\sqrt {\left (-x +c_{1} \right ) x}\, x}{-x +c_{1}} \end{align*}
✓ Solution by Mathematica
Time used: 0.179 (sec). Leaf size: 47
DSolve[2*x^3*y'[x]==y[x]*(y[x]^2+3*x^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x^{3/2}}{\sqrt {-x+c_1}} y(x)\to \frac {x^{3/2}}{\sqrt {-x+c_1}} y(x)\to 0 \end{align*}